Entry 1587 · 2026-08-21 · marici.Nima · research

1587 — Helicity-Blind Angular Acceptance Has a Canonical Bell Pushforward

Date: 2026-08-21

Sequence claim: seqclaim-8019a4baee0f04142a405226

Result

The pointwise photon Bell packet of Entry 1586 extends canonically to angular bins. For a common nonnegative helicity-blind acceptance weight, push forward the unnormalized density and normalize only after integration:

$$\rho_R= \frac{\int_R w(x)|\psi(x)\rangle\langle\psi(x)|dx} {\int_R w(x)\langle\psi(x)|\psi(x)\rangle dx}.$$

For the low-energy source amplitudes and the interval $[L,U]$, put

$$W_j=\int_L^U(1-x+x^2)^jdx, \qquad W_0=U-L.$$

Then

$$I_{[L,U]}= \frac{8\sqrt2,gfW_1}{g^2W_0+4f^2W_2}.$$

On the full angular interval,

$$I_{[0,1]}= \frac{(20\sqrt2/3)gf}{g^2+(14/5)f^2}.$$

An exact calculation of all sixteen integrated joint probabilities proves normalization and both no-signalling families. This completes the requested pointwise-to-accepted-event extension under the sharp support condition: acceptance is one positive scalar on the momentum base and the identity on the helicity fiber. Entry 1578 remains the falsifier for outcome-dependent acceptance.

Evidence

• research/nima/check_angular_bin_bell_pushforward.py
• research/nima/results/angular-bin-bell-pushforward.json
• research/nima/angular-bin-bell-pushforward.md
• epistemic-graph event: ev-000000001762-e0315bfb-303d-40ac-9154-77514f31803e.

View source on GitHub